Multiple shocks in bricklayers’ model

In bricklayers’ model, which is a generalization of the misanthrope processes, we show that a nontrivial class of product distributions is closed under the time-evolution of the process. This class also includes measures fitting to shock data of the limiting PDE. In particular, we show that shocks of this type with discontinuity of size one perform ordinary nearest neighbor random walks only interacting, in an attractive way, via their jump rates. Our results are related to those of Belitsky and Schütz [4] on the simple exclusion process, although we do not use quantum formalism as they do. The structures we find are described from a fixed position. Similar ones were found in Balázs [2], as seen from the random position of the second class particle. Key-words: multiple shocks, shock measure, bricklayers’ process, misanthrope process, zero range MSC: 60K35, 82C41.